Rotorcraft rotor hub assemblies include rotor blades joined together by a yoke. It may be advantageous to allow a pair of oppositely disposed rotor blades to flap or teeter in a seesaw motion about a teetering axis while the rotor hub assembly is rotating. Such flapping may be regulated by a flapping bearing disposed in the yoke between the pair of rotor blades. The flapping bearing may have radial and torsional spring rates that accommodate asymmetrical thrust between the pair of rotor blades as well as any Coriolis torque. While the radial and torsional spring rates of the flapping bearing may be tailored for these purposes, the flapping bearing may also have a propensity to move or deform in an axial direction along the teetering axis. Such deformation in the axial direction may cause unwanted contact between the flapping bearing and other components, leading to accelerated wear and tear. Also, because flapping bearings are primarily used to accommodate radial and torsional loads, it may be difficult to vary the composition of the flapping bearing to accommodate axial deformation without also affecting the radial and torsional spring rates. Accordingly, a need has arisen for an axial spring that can be easily appended to a flapping bearing and whose properties can be custom tailored to regulate stiffness in a single, axial direction to minimize the drawbacks of current flapping bearings.